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No. 4-3 REVIEWS OF BOOKS. 439 

of critical evaluation of some of the pieces listed. If the assumption 
were justified that everything mentioned is good, no objection could 
be raised. But certain of the pieces listed are notoriously treacherous, 
and this fact might well be remarked. A good many specific details 
might be called in question ; e. g., " The chronoscope should not vary 
in successive trials with such a mechanical device " (p. 191). This is 
a mere slip in form of statement, but it may well cause some ingenuous 
pioneer of a new laboratory to spend too much time trying to reach 
this goal, which, needless to say, no one ever has reached. If it could 
be attained, all the bother of computing variations could be abolished. 
On the same page there is, in connection with the mention of pendu- 
lum chronoscopes, no reference to Bergstrom's apparatus, which is by 
all odds much the best of the lot, so far as the reviewer knows. Other 
similar slips might be mentioned, but, as a whole, the book is excel- 
lent and most welcome. 

James R. Angell. 
University of Chicago. 

L'annee philosophique. Publiee sous la direction de F. Pillon. 
Paris, Felix Alcan, 1906. — pp. 301. 

Of the six articles of which this volume is composed, apart from M. 
Pillon's bibliography of the year, three relate to ancient and three to 
modern philosophy. Two of the former are concerned with Plato, 
who seems at last to be coming by his rights in the way of detailed 
study in France, as elsewhere, and one with Aristotle. M. Bro- 
chard writes of the ethics of Plato, and M. Rodier of the evolution 
of Plato's Dialectic. M. Brochard shows a thorough knowledge 
of the Platonic text, and his article affords a very useful and generally 
accurate and sympathetic account of the ethical teaching of the various 
dialogues. Certain objections might, however, be raised to some of 
his incidental utterances. It is doubtful whether he has not fallen at 
times, like most expositors of Plato, into the mistake of forgetting that 
a Platonic dialogue differs from a modern text-book of Philosophy in 
being first and foremost a work of dramatic art. Unless we keep this 
cardinal fact clearly before our minds, we are almost sure to make the 
mistake of taking what is merely the utterance of a dramatic figure, 
the ' Socrates ' or the ' Sophist ' of the dialogue, for a matter-of-fact 
statement of the writer's views, and so to overlook the vein of peculiar 
' irony ' which is as characteristic of Plato as of the great Athenian 
tragedians. I think M. Brochard has not always escaped this danger. 
For instance, the curious conclusion of the Protagoras, where both 


interlocutors are found to be contradicting the theses about the rela- 
tions between virtue and knowledge with which they set out, need not 
in the least imply, as M. Brochard thinks it does, any corresponding 
perplexity in the mind of Plato himself. It may well be no more than 
an example of ' irony, ' a dramatic illustration of the consequences 
of starting from postulates which are only half true. So, again, the 
conclusion in the Meno that virtue comes neither by nature nor from 
education, but by a sort of ' favor of Heaven, ' as is shown by the case 
of the famous Athenian statesmen who have never been able to trans- 
mit their 'virtue ' to their sons, is surely, in large part, satirical of a class 
of men about whose merits Plato was always sceptical. I think, too, 
that we do a grave injustice to Plato when we make him responsible 
for all that unwise admirers have read into his text as to the supposed 
immorality of the teachings of the 'Sophists.' As a fact, Plato never 
brings any general accusation of immoral teaching against the Sophists 
as a profession. He is careful to avoid any imputation on the upright- 
ness and honesty of the great Sophists, Protagoras and Gorgias, and 
the persons to whom M. Brochard refers as champions of immoralist 
views in the dialogues, Thrasymachus and Callicles, are not ' Sophists ' 
at all. One is a popular rhetorician, and the other a cultivated grand 
seigneur. The point is important, since it raises the whole question as 
to the sanity of Plato's judgments on contemporary society. I would 
further add that M. Brochard, perhaps out of respect for traditional 
verdicts, seems to me to be far too ready to take it as a matter of course 
that Aristotle's ethical views must necessarily show a great 'improve- 
ment ' when compared with those of his master. He hardly seems to 
realize how completely Aristotle's distinctive ethical doctrine comes 
straight out of the Philebus. 

M. Rodier's essay on the development of Plato's Dialectic is, as a 
whole, a most excellent piece of work. I would especially commend 
his crushing refutation of all the interpretations of Plato which, like 
that of Jowett, reduce the ' Ideas ' to concepts in the divine mind, or, 
like that of Lutoslawski, pretend to find evidence that ' Ideas ' have 
been replaced in the later dialogues by ' Souls ' as the supreme reali- 
ties. I cannot, however, understand why so sane a critic should have 
given in to the curious view that the Phcedrus is an earlier work than 
the Republic. To me, as to Raeder, it seems clear that the myth of 
the Phcedrus concerning the nature and destiny of the soul would 
have been hopelessly incomprehensible to readers who had not already 
the key to it furnished by the psychology of the Republic. What, 
e. g. , is to be made of the ' two horses ' which draw the chariot of the 

No. 4.] REVIEWS OF BOOKS. 44 1 

soul in the Pheedrus, apart from the psychological analyses of Republic, 
Bk. IV? In M. Rodier's explanation of the logical nature of the 
process Plato contemplated when he spoke of Dialectic, again, I find 
it hard to be satisfied with his identification of the ascending stage of 
Dialectic with an empirical process of establishment of more and more 
extensive genera of things by means of successive abstractions from 
sensible fact. It seems plain, I think, as a matter of language, that 
the demand that the process shall be accomplished "apart from all 
the senses," "without the aid of any sensible thing," is meant to 
apply just as much to the ascending as to the descending movement. 
Plato expressly says, in fact, that Dialectic is to take the objects 
studied by Geometry and Arithmetic as its starting-point. And he 
has said just before that, though geometers use sensible figures as aids 
to their studies, it is not these diagrams but the concepts they symbolize 
which are the real objects contemplated. Hence there can clearly be 
no element of the empirical anywhere in the dialectic process. What 
he really means seems to be this. The dialectician is to start with 
the various indefinables and unproved postulates of the mathe- 
matician as his data ; he is then to attempt the task of reducing their 
number until he comes at last to what is really absolutely indefinable 
and unprovable. Plato assumes that in the end there will be only 
one such absolutely simple first principle. This is the ascending part 
of the whole movement. We are then to deduce the relatively un- 
provable postulates of the several branches of pure science from the 
absolutely unprovable principle thus obtained by a regular chain of 
inferences ; and, similarly, to define the various undefinables of these 
sciences in terms of the ultimate undefinable discovered in the ascend- 
ing process. The procedure of modern ' Logistique, ' in reducing all 
the principles of Mathematics to those of Symbolic Logic, seems to 
me to afford an almost exact exemplification of the kind of thing 
which Plato is anticipating as the task of the philosophy of the 
future. The nearest analogue in the history of ancient thought would 
probably be the method followed by Proclus in his Theological Ele- 
ments. In any case, it is, I think, clear that no appeal to empirical 
sensible facts is supposed to play any part in the process at any stage. 
We cannot too often insist on the point that for Plato science is not 
the systematization of 'experience'; in his view, Science is always 
and necessarily ' transcendent ' of experience. Where experience 
begins, Science leaves off. We may not accept this view ourselves, 
we may even absolutely reject it ; but there is no eliminating it from 
the very centre of the Platonic theory of knowledge. 


The third article, by M. Hamelin, is devoted to a careful examina- 
tion of Aristotle's doctrine of the different forms of the ' opposition of 
concepts. ' The treatment of the subject is preponderantly expository 
rather than critical, and calls for no special comments here. I may 
note in passing one or two minor statements as to historical fact which 
are hardly exact. It is a mistake to say without qualification that Plato 
thought the difficulties raised by Antisthenes as to non-identical pre- 
dication trivial (" des pauvretes," p. 77). No doubt he did think so 
when he put them into the mouths of Euthydemus and Dionysodorus 
as specimens of their professional accomplishments ; but in the TTtece- 
tetus and Sophistes they are treated as very real problems, the resolution 
of which demands the full exercise of Plato's powers of logical analysis. 
The point is of some importance, since it is one of the pieces of evi- 
dence which show the comparatively late date of the Thetztetus, a 
result which is of the first significance for our whole conception of 
Plato's philosophical development. Nor is it quite true that Aristotle 
exclusively connects these logical problems with the Eleatic dialectic. 
He expressly connects the theory that ' contradiction is impossible ' 
also with the relativism of Protagoras {Met., ioo9a6) and indirectly 
with Heracliteanism (ib., ioosb25). 

The two articles dealing with modern philosophy are one by M. 
Pillon on the philosophy of Renouvier, in connection with the recent 
book of M. Seailles on that subject, and one by M. Dauriac on the 
philosophy of M. Tarde. I cannot think that M. Pillon is altogether 
happy in his attempt to meet the criticisms which have been passed 
upon the finitist assumptions of Neo-criticism. He appears to hold 
that the Law of Contradiction is somehow a more ultimate and im- 
portant principle than any of the other laws of Logic. He thinks, 
again, if I understand him correctly, that the notion of cardinal num- 
ber is already logically implied by the notions of a term and of a class 
of terms. And he assumes that whatever has a cardinal number has a 
finite number. All these assumptions are, to say the least of it, re- 
jected by a great and growing school of mathematical thinkers, and 
require considerable justification before they can be admitted as axioms 
in philosophy. The Law of Contradiction has been fairly shown to be 
only one among a plurality of axioms, all of which are indispensable 
to valid inference. When I say, "A is an X, B is an X, and A is not 
identical with B," I surely have already the concepts of a term, of a 
plurality of terms, and of a class ; yet there is no reference in the propo- 
sition to any concept of cardinal number. In fact, I could go on 
to use the statement in constructing a definition of the number '2,' to 

No. 4.] REVIEWS OF BOOKS. 443 

which it must therefore be logically prior. And, finally, it is a pure 
assumption that whatever has a number must be denumerable, /. e., 
that the number of any actual collection must be finite. What, e . g. , 
is the number of the whole series of finite integers ? It clearly has no 
finite number, yet there is equally clearly an entity connected with it 
in the same way in which the number of a finite collection is connected 
with that collection. It is greater than any finite number, less than 
the entity which we call the ' number ' of all the real numbers, is sub- 
ject to formal laws of addition and multiplication, and so forth. To 
recognize its existence while refusing to give it the name of a ' number ' 
is merely to dispute about words. To deny its existence is impossible, 
at least for M. Pillon, who rightly denies that we create the ' number ' 
of a collection for ourselves by the process of counting. No logical 
ground then has been given for denying the existence of collections 
with an infinite number of terms. Hence the statement that no con- 
tinuum can be objectively real, and that space, in particular, is shown 
to be subjective by the single consideration that it is a continuum, is a 
pure petitio principii. Nor should M. Pillon have simply taken it for 
granted that all continua are in the end spatial, without some consider- 
ation of the modern doctrines which construct the continuum out of 
discrete elements and maintain that the only certain continuum with 
which we are acquainted is non-spatial, viz., the arithmetical continuum 
of the real numbers. It is possible for us to agree heartily with the 
greater part of the article, in which the author is engaged in defending 
the reality of the categories of personal experience, in other words the 
reality of teleology, against current phenomenalism, without according 
any faith either to the alleged finitude of all actual collections, or ad- 
mitting the illusory character of space. 

The essay on the philosophy of Tarde could only be discussed by one 
who has a closer acquaintance with the subject than the present writer. 

A. E. Taylor. 
McGill University.